It will run, yes.
Whether it will run fast and smoothly enough to suit you... well... only YOU will be able to tell us that, after you've tried it.
WARNING DANGER WARNING
Before you upgrade, I would strongly suggest that you create a bootable cloned backup of your internal drive AS IT IS NOW. You can do this by using either CarbonCopyCloner or SuperDuper. Both are free to download and use for 30 days. I prefer CCC because it can also clone your recovery partition as well.
Of course, you'll need an external drive with which to do this.
If for some reason you DON'T like the way High Sierra runs, and you want to "get back, get back, get back to where you once belonged", do this:
1. Boot from the backup
2. Erase the internal drive (wipe it out!)
3. RE-clone the backup drive BACK TO the internal drive.
If you don't have a cloned backup, be prepared for a mountain of frustration and trouble to get back...